Problem: What is the greatest common factor of $14c^{3}$, $70c^{4}$, and $28c^{2}$ ?
Let's factor each monomial to its prime factors: $\begin{aligned} 14c^{3}&=(2)(7)(c)(c)(c) \\\\ 70c^{4}&=(2)(5)(7)(c)(c)(c)(c) \\\\ 28c^{2}&=(2)(2)(7)(c)(c) \end{aligned}$ We want the largest set of factors that's included in all three monomials. All of the monomials have one factor of $ 2$, one factor of $ 7$, and two factors of $ c$ : $\begin{aligned} 14c^{3}&=( 2)( 7)( c)( c)(c) \\\\ 70c^{4}&=( 2)(5)( 7)( c)( c)(c)(c) \\\\ 28c^{2}&=( 2)(2)( 7)( c)( c) \end{aligned}$ This is the greatest common factor: $( 2)( 7)( c)( c)=14c^{2}$